Will a new router provide better multiplexing?

[irishScott]

My dad's work requires that he be connected to a VPN. While this typically doesn't take up much bandwidth, it still maintains a constant connection through our old B router (that Verizon gave us way back when).

Thing is, whenever I try to play any online games while I'm home and he's home, I get serious lag, despite the fact that the connection only taking a couple of KBs/s of bandwidth. Would a new router help things? Scoured my router's drivers, no luck with anything related to multiplexing/throttling.